Initial boundary value problem for a class of non-linear strongly damped wave equations

The paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non-linear wave equations. By a H-0(k)-Galerkin approximation scheme, it proves that the above-mentioned problem admits a unique classical solution depending continuously on initial data and decaying to zero as t --> +infinity as long as the non-linear terms are sufficiently smooth; they, as well as their derivatives or partial derivatives, are of polynomial growth order and the initial energy is properly small. Copyright (C) 2003 John Wiley Sons, Ltd.